The Climate Crisis

No, removing livestock will generally lead to increased vegetation and biodiversity, longer growth and more photosynthesis. There would be an increase in plant litter leading to increased microbial activity - releasing some carbon as CO2, and sequestering most of the rest in the soil.

Methane production would occur in anaerobic conditions (e.g. waterlogged or more compacted soil,) but nowhere near as efficiently as it does in the rumen of livestock.